Finite Group Databasebeta

← #13130859

Subgroups — #13130859

Order 1664.

378 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88237C211yesmaximal, characteristic, complemented
2C2×#88137C211yesmaximal, characteristic
3C2×#88119C212yesmaximal
4#11719135C211yesmaximal, characteristic, complemented
5#11718289C212yesmaximal, complemented
6C22×C22⋊D13C2211yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261C2212yes—
9C2×C22⋊#261C2212yes—
10#88237—24no—
11C2×C4⋊#261—21no—
12C2×C4×#261—21no—
13C2×C13×C22⋊C4C411yescharacteristic, complemented
14C2×C22⋊Dic13C411yescharacteristic, complemented
15C2×#6103C2211yescharacteristic
16C2×C4⋊Dic13C411yescharacteristic, complemented
17C2×#6101C411yescharacteristic, complemented
18#88137—21no—
19#88137—21no—
20#88137—21no—
21#88137—21no—
22#88119—24no—
23(C2×#261)⋊C4—21no—
24(C2×#261)⋊C4—21no—
25C24×C13C2×C411yescharacteristic
26C23×D13C2311yescharacteristic
27C22×#261—22no—
28C22×#261—22no—
29C22×C4×C13C2×C411yescharacteristic
30C22×C4×C13C2×C411yescharacteristic
31C2×C22⋊D13—22no—
32C2×C22⋊D13—21no—
33C2×C22⋊D13—21no—
34C2×C22⋊D13—22no—
35C22×Dic13C2×C411yescharacteristic
36C22×Dic13C2×C411yescharacteristic
37C22×Dic13C2×C411yescharacteristic
38C2×C4×D13—22no—
39C2×C4×D13—22no—
40C2×C4×D13D411yescharacteristic
41C2×C4×D13D411yescharacteristic
42C2×C4×D13D411yescharacteristic
43C2×C4×D13D411yescharacteristic
44C22⋊#261—22no—
45C22⋊#261—22no—
46C22⋊#261—22no—
47C22⋊#261D414yes—
48C4⋊#261—24no—
49C4×#261—24no—
50C13×C22⋊C4—21no—
51C13×C22⋊C4—21no—
52C22⋊Dic13—21no—
53C22⋊Dic13—21no—
54#6103—21no—
55#6103—21no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58#6101—21no—
59#6101—21no—
60#1899—131nomaximal, Sylow
61C23×C13—21no—
62C23×C13—22no—
63C23×C13—41no—
64C23×C13—41no—
65C23×C13C22×C411yescharacteristic
66C22×D13—41no—
67C22×D13—41no—
68C22×D13C2×D411yescharacteristic
69C22×D13C2×D411yescharacteristic
70C22×D13C2×D412yes—
71C22×D13#4112yes—
72C2×#261—24no—
73C2×#261—42no—
74C2×#261—42no—
75C2×#261—42no—
76C2×#261—42no—
77C2×#261—42no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—41no—
81C2×C4×C13C22⋊C411yescharacteristic
82C2×C4×C13C22⋊C411yescharacteristic
83C22⋊D13—41no—
84C22⋊D13—42no—
85C22⋊D13—41no—
86C2×Dic13—22no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—41no—
91C2×Dic13C22⋊C411yescharacteristic
92C2×Dic13C22⋊C411yescharacteristic
93C4×D13—21no—
94C4×D13—21no—
95C4×D13—22no—
96C4×D13—22no—
97C4×D13—21no—
98C4×D13—21no—
99C2×#123—131no—
100C2×#117—131no—
101C2×#99—132no—
102#381—131no—
103#342—132no—
104C22×C13—21no—
105C22×C13—21no—
106C22×C13—41no—
107C22×C13—41no—
108C22×C13—41no—
109C22×C13—82no—
110C22×C13C2×C22⋊C411yescharacteristic
111C22×C13C4×D412yes—
112C2×D13—21no—
113C2×D13—21no—
114C2×D13—21no—
115C2×D13—21no—
116C2×D13—42no—
117C2×D13—42no—
118C2×D13#12011yescharacteristic
119C2×D13#12112yes—
120C2×D13#12311yescharacteristic
121#261—44no—
122#261—82no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—41no—
126Dic13—21no—
127Dic13—21no—
128Dic13—41no—
129Dic13—41no—
130C22×D4—131no—
131C23×C4—131no—
132#123—261no—
133#123—261no—
134#123—261no—
135#123—261no—
136#117—264no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—131no—
139C2×C4⋊C4—261no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4—131no—
142C2×C22⋊C4—131no—
143C2×C22⋊C4—132no—
144C2×C22⋊C4#26111yescharacteristic, complemented
145C2×C42—261no—
146#99—264no—
147#95—261no—
148#95—261no—
149C2×C13—22no—
150C2×C13—81no—
151C2×C13#38611yescharacteristic
152C2×C13#41011yescharacteristic
153C2×C13#41011yescharacteristic
154D13—21no—
155D13—22no—
156D13—21no—
157C24—131no—
158C24C2×#26111yescharacteristic
159C2×D4—262no—
160C2×D4—261no—
161C2×D4—261no—
162C2×D4—262no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—262no—
171C22×C4—262no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4C2×#26111yescharacteristic
175C22×C4C2×#26111yescharacteristic
176C4⋊C4—261no—
177C4⋊C4—261no—
178C4⋊C4—264no—
179C4⋊C4—261no—
180C4⋊C4—261no—
181C22⋊C4—21no—
182C22⋊C4—21no—
183C22⋊C4—134no—
184C22⋊C4—261no—
185C22⋊C4—261no—
186C22⋊C4—261no—
187C22⋊C4—261no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C22⋊C4—262no—
191C42—264no—
192C13#189911yescharacteristic, complemented, Sylow
193C23—21no—
194C23—22no—
195C23—41no—
196C23—41no—
197C23—131no—
198C23—131no—
199C23—132no—
200C23—132no—
201C23—521no—
202C23—521no—
203C23C22×#26111yescharacteristic
204D4—521no—
205D4—522no—
206D4—521no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—131no—
211C2×C4—131no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—261no—
217C2×C4—261no—
218C2×C4—262no—
219C2×C4—264no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—521no—
226C2×C4—522no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4C22⋊#26111yescharacteristic
230C2×C4C22⋊#26111yescharacteristic
231C22—21no—
232C22—21no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—82no—
237C22—131no—
238C22—132no—
239C22—131no—
240C22—261no—
241C22—261no—
242C22—261no—
243C22—261no—
244C22—522no—
245C22—522no—
246C22D4×#26112yes—
247C22C2×C22⋊#26111yescharacteristic
248C4—21no—
249C4—21no—
250C4—41no—
251C4—261no—
252C4—261no—
253C4—524no—
254C4—521no—
255C4—521no—
256C4—1042no—
257C2—22no—
258C2—81no—
259C2—261no—
260C2—262no—
261C2—261no—
262C2#1171911611yescharacteristic
263C2#1171914211yescharacteristic
264C2#1171915011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C22⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC22×C22⋊D13C22
cosocleC23×D13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#1899
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#88237C2semidirect
4. #11719135C2semidirect
5. #11718289C2semidirect
13. C2×C13×C22⋊C4C4semidirect
14. C2×C22⋊Dic13C4semidirect
16. C2×C4⋊Dic13C4semidirect
17. C2×#6101C4semidirect
144. C2×C22⋊C4#261semidirect
192. C13#1899semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#882372
C2×#881372
C2×#881192
#117191352
#117182892
#189913